On directed packing designs with block size 5 and index λ = 2

Abstract

Let υ, κ and λ be positive integers. A (υ,κ,λ) directed packing design, denoted by DP(υ,κ,λ), is a (υ,κ,2λ) packing design in which blocks are regarded as transitively ordered κ-tuples and in which each ordered pair of elements appears in at most λ blocks. The directed parking problem is to determine the maximum number of blocks, DD(υ,κ,λ) in a directed packing design. In this paper, this problem is completely solved for the case κ = 5, λ = 2 and υ ≥ 5.